1*7f296bb3SBarry Smith(integrator_table)= 2*7f296bb3SBarry Smith 3*7f296bb3SBarry Smith# Summary of Time Integrators Available In PETSc 4*7f296bb3SBarry Smith 5*7f296bb3SBarry Smith```{eval-rst} 6*7f296bb3SBarry Smith.. list-table:: Time integration schemes 7*7f296bb3SBarry Smith :name: tab_TSPET 8*7f296bb3SBarry Smith :header-rows: 1 9*7f296bb3SBarry Smith 10*7f296bb3SBarry Smith * - TS Name 11*7f296bb3SBarry Smith - Reference 12*7f296bb3SBarry Smith - Class 13*7f296bb3SBarry Smith - Type 14*7f296bb3SBarry Smith - Order 15*7f296bb3SBarry Smith * - euler 16*7f296bb3SBarry Smith - forward Euler 17*7f296bb3SBarry Smith - one-step 18*7f296bb3SBarry Smith - explicit 19*7f296bb3SBarry Smith - :math:`1` 20*7f296bb3SBarry Smith * - ssp 21*7f296bb3SBarry Smith - multistage SSP :cite:`ketcheson_2008` 22*7f296bb3SBarry Smith - Runge-Kutta 23*7f296bb3SBarry Smith - explicit 24*7f296bb3SBarry Smith - :math:`\le 4` 25*7f296bb3SBarry Smith * - rk* 26*7f296bb3SBarry Smith - multiscale 27*7f296bb3SBarry Smith - Runge-Kutta 28*7f296bb3SBarry Smith - explicit 29*7f296bb3SBarry Smith - :math:`\ge 1` 30*7f296bb3SBarry Smith * - beuler 31*7f296bb3SBarry Smith - backward Euler 32*7f296bb3SBarry Smith - one-step 33*7f296bb3SBarry Smith - implicit 34*7f296bb3SBarry Smith - :math:`1` 35*7f296bb3SBarry Smith * - cn 36*7f296bb3SBarry Smith - Crank-Nicolson 37*7f296bb3SBarry Smith - one-step 38*7f296bb3SBarry Smith - implicit 39*7f296bb3SBarry Smith - :math:`2` 40*7f296bb3SBarry Smith * - theta* 41*7f296bb3SBarry Smith - theta-method 42*7f296bb3SBarry Smith - one-step 43*7f296bb3SBarry Smith - implicit 44*7f296bb3SBarry Smith - :math:`\le 2` 45*7f296bb3SBarry Smith * - bdf 46*7f296bb3SBarry Smith - Backward Differentiation Formulas 47*7f296bb3SBarry Smith - one-step 48*7f296bb3SBarry Smith - implicit 49*7f296bb3SBarry Smith - :math:`\le 6` 50*7f296bb3SBarry Smith * - alpha 51*7f296bb3SBarry Smith - alpha-method :cite:`jansen_2000` 52*7f296bb3SBarry Smith - one-step 53*7f296bb3SBarry Smith - implicit 54*7f296bb3SBarry Smith - :math:`2` 55*7f296bb3SBarry Smith * - gl 56*7f296bb3SBarry Smith - general linear :cite:`butcher_2007` 57*7f296bb3SBarry Smith - multistep-multistage 58*7f296bb3SBarry Smith - implicit 59*7f296bb3SBarry Smith - :math:`\le 3` 60*7f296bb3SBarry Smith * - eimex 61*7f296bb3SBarry Smith - extrapolated IMEX :cite:`constantinescu_a2010a` 62*7f296bb3SBarry Smith - one-step 63*7f296bb3SBarry Smith - IMEX 64*7f296bb3SBarry Smith - :math:`\ge 1`, adaptive 65*7f296bb3SBarry Smith * - dirk 66*7f296bb3SBarry Smith - DIRK 67*7f296bb3SBarry Smith - diagonally implicit Runge-Kutta 68*7f296bb3SBarry Smith - implicit 69*7f296bb3SBarry Smith - :math:`\ge 1` 70*7f296bb3SBarry Smith * - arkimex 71*7f296bb3SBarry Smith - See :any:`tab_IMEX_RK_PETSc` 72*7f296bb3SBarry Smith - IMEX Runge-Kutta 73*7f296bb3SBarry Smith - IMEX 74*7f296bb3SBarry Smith - :math:`1-5` 75*7f296bb3SBarry Smith * - rosw 76*7f296bb3SBarry Smith - See :any:`tab_IMEX_RosW_PETSc` 77*7f296bb3SBarry Smith - Rosenbrock-W 78*7f296bb3SBarry Smith - linearly implicit 79*7f296bb3SBarry Smith - :math:`1-4` 80*7f296bb3SBarry Smith * - glee 81*7f296bb3SBarry Smith - See :any:`tab_IMEX_GLEE_PETSc` 82*7f296bb3SBarry Smith - GL with global error 83*7f296bb3SBarry Smith - explicit and implicit 84*7f296bb3SBarry Smith - :math:`1-3` 85*7f296bb3SBarry Smith * - mprk 86*7f296bb3SBarry Smith - Multirate Partitioned Runge-Kutta 87*7f296bb3SBarry Smith - multirate 88*7f296bb3SBarry Smith - explicit 89*7f296bb3SBarry Smith - :math:`2-3` 90*7f296bb3SBarry Smith * - basicsymplectic 91*7f296bb3SBarry Smith - Basic symplectic integrator for separable Hamiltonian 92*7f296bb3SBarry Smith - semi-implicit Euler and Velocity Verlet 93*7f296bb3SBarry Smith - explicit 94*7f296bb3SBarry Smith - :math:`1-2` 95*7f296bb3SBarry Smith * - irk 96*7f296bb3SBarry Smith - fully implicit Runge-Kutta 97*7f296bb3SBarry Smith - Gauss-Legrendre 98*7f296bb3SBarry Smith - implicit 99*7f296bb3SBarry Smith - :math:`2s` 100*7f296bb3SBarry Smith``` 101*7f296bb3SBarry Smith 102*7f296bb3SBarry Smith```{eval-rst} 103*7f296bb3SBarry Smith.. bibliography:: /petsc.bib 104*7f296bb3SBarry Smith :filter: docname in docnames 105*7f296bb3SBarry Smith``` 106